Question: Rewrite as a simplified fraction. ${0.5\overline{20} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 520.202...\\ 10x &= 5.202...\end{align*}}$ Subtracting the two equations, we have: ${990x = 515}$ ${x = \dfrac{515}{990}} $ ${x = \dfrac{103}{198}} $